extricate,
An automatic go around is not available any time after the aircraft touches down during landing, because the TOGA switches will be inhibited. If a go around is required after touch down, it must be performed manually, without flight director guidance. The TOGA switches become active again shortly after the aircraft becomes airborne again (2 seconds??). Thereafter, pressing the TOGA switches will restore the flight directors in TOGA mode.
I believe the reason for the inhibit is a certification requirement to prevent inadvertent activation of TOGA mode during a normal landing, which could cause a runway overrun if not handled correctly.